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A Cornucopia of Nanoscale Ordered Phases in Sphere Forming Tetrablock Terpolymers Siddharth Chanpuriya, Kyungtae Kim, Jingwen Zhang, Sangwoo Lee, Akash Arora, Kevin D. Dorfman, Kris T. Delaney, Glenn H. Fredrickson, and Frank S Bates ACS Nano, Just Accepted Manuscript • Publication Date (Web): 07 Apr 2016 Downloaded from http://pubs.acs.org on April 8, 2016

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A Cornucopia of Nanoscale Ordered Phases in Sphere Forming Tetrablock Terpolymers Siddharth Chanpuriya,a Kyungtae Kim,a Jingwen Zhang,a† Sangwoo Lee,b Akash Arora,a Kevin D. Dorfman,a Kris T. Delaney,c Glenn H. Fredricksonc and Frank S. Batesa‡ a

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455; bDepartment of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180; cMaterials Research Laboratory, University of California, Santa Barbara, CA 93106. † ‡

Currently at ExxonMobil Chemical Company, Baytown, TX 77520. Corresponding author: FSB, [email protected].

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Abstract We report the phase behavior of a series of poly(styrene)-b-poly(isoprene)-b-poly(styrene)′-bpoly(ethylene oxide) (SIS′O) tetrablock terpolymers. This study was motivated by self-consistent field theory (SCFT) calculations that anticipate a rich array of sphere forming morphologies with variations in the molecular symmetry parameter = /( + ), where N is the block degree of polymerization and the volume fraction of O is less than about 0.22. Eight SIS′O samples, with τ ranging from 0.21 to 0.73 were synthesized and investigated using small-angle X-ray scattering and transmission electron microscopy, yielding evidence of nine different spherical phases: hexagonal (HEXS), FCC, HCP, BCC, rhombohedral (tentative), liquid-like packing (LLP), dodecagonal quasicrystal (DDQC), and Frank-Kasper σ and A15 phases. At temperatures close to the order-disorder transition, these tetrablocks behave as pseudo [SIS′]-O diblocks and form equilibrium morphologies mediated by facile chain exchange between micelles. Transition from equilibrium to non-equilibrium behavior occurs at a temperature (Terg) several tens of degrees below the order-disorder transition temperature, speculated to be coincident with the loss of ergodicity as chain exchange is arrested due to increased segregation strength between the core (O) and corona (SIS′) blocks. Non-equilibrium ordered structures form when T < Terg; these are interpreted using SCFT calculations to elucidate the free energy landscape driving ordering in the S and I block matrix. These experiments demonstrate a profound dependence on phase stability with variations in τ and temperature, providing insights into the formation of ordered phase symmetry in this class of asymmetric multiblock polymers.

Keywords: multiblock polymer, phase behavior, self-consistent field theory, Frank-Kasper phases, quasicrystal

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Block polymers are macromolecules that contain discrete sequences of chemically distinct repeat units that can segregate into periodic nanoscale structures containing various domain geometries. The simplest molecular architecture in this class of self-assembling materials is the AB diblock copolymer, which has been extensively studied. In his seminal 1980 publication, Leibler developed a mean-field theory of phase equilibria in AB diblocks based on just two parameters: the product χABN, termed the segregation strength, and fA, the volume fraction of block A.1 The domain geometry and ordered state symmetry are controlled primarily by fA when χABN >> 10, denoted strong segregation, whereas the order-disorder transition (ODT) boundary depends on both parameters. Only three ordered phases were found to be stable near the ODT: onedimensional lamellae (LAM), two-dimensional hexagonally ordered cylinders (HEXC), and a three-dimensional body-centered cubic (BCC) arrangement of spheres. Subsequent experiments confirmed the now ubiquitous sphere-forming BCC phase in many diblock copolymer systems.2– 4

We note that, while these domains are frequently referred to as spheres, they are actually soft

polyhedral particles with facets dictated by the lattice symmetry and the necessity to fill space at uniform density;5–8 for simplicity we refer to the morphology as spherical. Subsequent refinements of Leibler’s treatment based on the framework of self-consistent field theory (SCFT) have accounted for additional phases in diblocks (e.g., Gyroid9 and O70 10), and a rich assortment of morphologies in triblock terpolymers11–14 and higher functionality multiblocks. In many cases, these theoretical developments have been motivated by experimental findings15–20 driving subsequent expanded synthetic and structural characterization efforts that lead to additional insights.21 Recent discovery of the complex low symmetry Frank-Kasper σ phase in an asymmetric diblock copolymer22 spawned another such cycle, where Xie et al. identified


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conformational asymmetry as a key ingredient for stabilizing this fascinating quasicrystal approximant.23

Advances in polymer synthetic chemistry have opened virtually unbounded vistas for creating multiblock polymers with nearly unlimited design flexibility. However these extraordinary opportunities create a daunting dilemma: what should be made? Increasing the number of blocks and the diversity of block chemistries leads to a rapid escalation in the degrees of freedom, even if we limit ourselves to single component materials.24 For example, a tetrablock molecular architecture built from three different repeat units affords access to nine distinct block sequences (ABAC, ABCA, ACAB, etc.) each offering independent control over the block molecular weights and hence composition. Selection of the block chemistries sets the three (temperature dependent) segment-segment interaction parameters (χAB, χAC, and χBC) that control the segregation strength. Clearly, the paradigm of experimentally driven theory needs to be inverted if we have any hope of exploiting the remarkable opportunities for materials design afforded by polymer science and engineering. This article describes a recent collaboration, driven by the Materials Genome Initiative (MGI), to accomplish this goal.

We selected poly(styrene)-b-poly(isoprene)-b-poly(styrene)′-b-poly(ethylene oxide) (SIS′O) tetrablock terpolymers as an exceptional target opportunity. This type of multiblock has been shown to produce several intriguing morphologies in the limit of a minority of O and equal size S blocks, including the σ and dodecagonal quasicrystal (DDQC) phases.22,25 We identified the molecular symmetry parameter = /( + ) as a prime candidate for investigation. SCFT calculations indicated that the window of sphere forming morphologies was highly sensitive to and anticipated new modes of ordering. Guided by these calculations, we synthesized a series of


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eight SIS′O polymers using anionic polymerization; Figure 1 depicts the molecular structure and the distribution of blocks in the core and corona of the associated domains. Small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) experiments revealed an extraordinarily rich complement of packing symmetries, nine in total, as a function of temperature and τ, reflecting both equilibrium and metastable states. These results indicate a transition from ergodic to non-ergodic behavior with the development of strong segregation as the temperature is lowered below the order-disorder transition temperature (TODT). We associate this transition, at a temperature denoted Terg, with the rapid extinction of chain exchange (diffusion) as the temperature is reduced and the penalty for moving O blocks through the S′IS matrix increases dramatically.26,27 SCFT calculations suggest that repositioning of the S and I blocks influences the formation of metastable states when T < Terg.

The findings and interpretations reported here provide important insights into several aspects of nanostructure formation in soft materials. Perhaps most significant is a demonstration of the power derived from directly coupling theory and experiment in the quest for efficient materials design. Identification of the remarkable impact of the molecular symmetry parameter τ reinforces the notion that multiblock copolymers offer unparalleled possibilities for creating precisely tailored morphologies. More broadly, we believe knowledge gained by understanding this class of matter will inform theory and simulation28–30, and experiments on other classes of self-assembling soft materials such as surfactants,31–33 lipids,34–37 hybrid nanoparticles,38–40 and dendrimers,41–44 and has the potential to provide a better fundamental understanding of the factors responsible for the formation of low symmetry phases and aperiodic quasicrystals in hard materials.8,45–48


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Figure 1. (a) Molecular structure of the SIS′O tetrablock terpolymer and (b) core-shell sphere domain structure showing terminal SI blocks that can loop, bridge, or intermix.

Results

In order to examine the effect of asymmetry in length of S and S′, we begin with the calculation of phase boundaries as a function of the parameter τ at constant fS/fI, where fS accounts for both poly(styrene) blocks. Here, = /( + ) in which NS and NS′ are the degrees of polymerization of the terminal and internal poly(styrene) blocks, respectively. Figure 2 shows the SCFT-computed phase boundaries for different asymmetry values in the range 0.2 < τ < 0.9. Here we are primarily interested in the phase behavior of (nominally) sphere-forming phases, so we omit the calculation of phase transitions for the non-sphere forming region. The calculations were done at T = 180 °C with the interaction parameters given in the methods section, and the degree of polymerization calculated using experimentally reported molecular weights and densities. Moreover, the calculation was done in a manner that mimics experiments: the volume fraction fO in Figure 2 corresponds to the amount of PEO added to a parent SIS′ triblock for the isopleth, fS/fI = 0.93.


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Figure 2. Order-disorder and order-order transitions for different values of the asymmetry, τ = NS/(NS+NS′) from SCFT calculations at 180 °C. Results indicate the window for sphere-forming phases dramatically widens around τ = 0.7, prompting experiments in this region of phase space. The calculations are done for fS/fI = 0.93 isopleth with parent SIS′ triblock molecular weight, Mn = 20.8 kDa that corresponds to N = 298.5. The degree of polymerization is obtained by using the reference volume, vref = 118 Å3, and the densities reported at T = 140 °C.49

The phase diagram in Figure 2 was constructed by considering face-centered cubic (FCC), bodycentered cubic (BCC), hexagonally close packed (HCP), Frank-Kasper A15 (A15), and FrankKasper σ (σ) phases as the competing sphere-forming morphologies along with the disordered and hexagonally packed cylinder (HEXC) phases (see Figure 8 below for illustrations50 of these phases). The triple points shown in Figure 2 were determined from a combination of estimating boundaries and bracketing where phases collapsed. We observed that the A15 phase is never the stable phase but competes with the σ phase throughout the phase diagram with a difference in free energy of approximately 1 10 kBT per chain. Because of such a minute difference in the free energies, marginal changes in the interaction parameters might stabilize the A15 phase over the σ phase or may produce a triple point exhibiting a coexistence of A15 and σ with any other (BCC, FCC, HCP) sphere-forming phase. Nevertheless, Figure 2 demonstrates that the τ parameter has a significant effect on phase boundaries; an increase in τ widens the phase window 7 ACS Paragon Plus Environment

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for sphere-forming phases, providing room to enclose a host of different packing arrangements including the complex σ phase.

Table 1. Characterization data for reported SIS′O tetrablock terpolymers.

Polymer

Mn, kDaa

Mw/Mnb

fS

fI

fO

τ

TODT, °Cd

SIS′O-0.21

19.7

1.04

0.40

0.44

0.16

0.21

>250

SIS′O-0.32

19.1

1.07

0.48

0.46

0.07

0.32

153

SIS′O-0.39

17.0

1.04

0.46

0.47

0.07

0.39

130

SIS′O-0.50

23.0

1.04

0.46

0.46

0.08

0.50

196

SIS′O-0.61

24.2

1.05

0.45

0.46

0.09

0.61

177

SIS′O-0.68

21.5

1.04

0.43

0.43

0.14

0.68

285e

SIS′O-0.70

20.7

1.14

0.43

0.45

0.12

0.70

177

SIS′O-0.73

22.4

1.03

0.42

0.45

0.13

0.73

284e

a

Calculated using a combination of SEC and 1H NMR spectroscopy data. bDetermined through SEC. Volume fractions calculated from 1H NMR spectroscopy data using reported melt densities at 140 °C.49 d Obtained using DMS eObtained using SAXS c

Motivated by these theoretical results, the experimental counterpart to this study focuses on the phase behavior of eight SIS′O samples with varying asymmetry in the lengths of the terminal and internal polystyrene blocks (denoted S and S′, respectively). This asymmetry, quantified by the τ parameter, is varied experimentally from 0.21 to 0.73, which includes the widest sphere forming region observed in the SCFT simulations around τ = 0.7. All SIS′-OH precursors fall approximately on the same fS/fI = 1 isopleth with the fO in subsequent tetrablocks being varied between 0.07 to 0.16. A detailed summary of molecular characterization for all samples is provided in Table 1. All samples discussed here are referred to as SIS′O-τ. Polymer morphology was mainly characterized using a combination of SAXS and TEM, above 100 °C and on specimens quenched from this temperature range to below the glass transition temperature, respectively. All measurements correspond to conditions well above the poly(styrene) glass


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transition; in all specimens Tg,SIS′ < 70 °C due to mixing of the S and I blocks. The following paragraphs report the phase behavior observed in these samples as the asymmetry parameter, τ, was increased.

Figure 3. Representative (a) SAXS patterns and (b) TEM image from SIS′O-0.32. Labels identify the relative peak positions associated with a hexagonal symmetry. The TEM image reveals large grains of sphere forming tetrablocks oriented on hexagonal and square lattices. SAXS patterns and TEM images of SIS′O-0.21 reveal similar behavior.

Throughout the temperature range of 100 – 250 °C for SIS′O-0.21 and 100 – 150 °C for SIS′O0.32, the scattering patterns display peaks at (q/q*)2 = 1, 3, and 4 with q* being the location of the primary peak (Figures S1a and 3a). These peaks are consistent with hexagonal (P6mm) symmetry. For SIS′O-0.32, above 150 °C the scattering pattern displays a single broad peak indicative of a state of disorder (Figure 3a). However, a surprising result is obtained from the TEM micrographs of this polymer: the microdomains are spherical instead of the expected cylinders and contain regions of 4- and 6-fold symmetry (Figure 3b). SIS′O-0.21 displays the same domain geometry as well (Figure S1b,c). These results parallel findings in another set of SISO tetrablocks on the fS/fI = 2/3 isopleth, where varying fO from 0.09 to 0.19 produced spherical microdomains on a lattice also consistent with hexagonal P6mm space group 9 ACS Paragon Plus Environment

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symmetry. (Zhang and Bates interpreted the SAXS and TEM images, identical to those shown here for SIS′O-0.21 and SIS′O-0.32 as evidence for a simple hexagonal crystal structure with P6/mmm symmetry.51 We now question that tentative interpretation and emphasize that the true crystallographic assignment for this morphology has not been definitively established.) This packing is referred to here as hexagonally packed spheres (HEXS) to avoid confusion with HCP or HEXC morphologies.

Figure 4. (a) SAXS patterns obtained from SIS′O-0.39. Relative peak positions associated with hexagonal symmetry at 100 °C are labeled. The σ phase and disordered states are observed upon heating. TEM images obtained after annealing at (b) 100 °C (with Fourier transform) and (c) 120 °C. The morphology in (c) is consistent with the σ phase and the characteristic σ-element with 32.4.3.4 tiling is highlighted.

SAXS data for SIS′O-0.39 was collected in the 100 – 140 °C temperature range (Figure 4a). While heating, the sample shows reflections consistent with a HEXS assignment at 100 °C, further supported by large regions that exhibit 6-fold symmetry in TEM images (Figure 4b and inset Fourier transform). Although the TEM images reveal large grains of well-ordered spheres, peaks observed in the SAXS patterns are quite broad; this discrepancy most probably derives from a difference in annealing times for the SAXS (ca. 5 min.) and TEM (24 h) samples. Upon heating to 120 °C, the sample develops a scattering pattern consistent with that of the σ phase before disordering at 140 °C with the disappearance of all Bragg peaks. A representative TEM image obtained from a specimen annealed at 120 °C is shown in Figure 4c where the 10 ACS Paragon Plus Environment

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characteristic 32.4.3.4 tiling of the σ phase is highlighted. Adjusting the τ parameter to 0.5 results in a tetrablock containing symmetric interior and terminal poly(styrene) chain lengths; this sample was extensively characterized in previous publications (referred to as SISO-3).22,52 The associated core-shell particles display liquid-like packing (LLP) at lower temperatures and the σ phase between 140 – 224 °C before disordering at yet higher temperatures. A detailed structural understanding of the LLP state remains elusive but it seems to be characterized by regions of short-range correlated microdomain packing while lacking long-range order (a representative TEM image is shown in Figure 5b). It is important to note that this state can be achieved either by heating from a freeze-dried state (as shown for SIS′O-0.50) or cooling from the equilibrium disordered phase at a rate rapid enough to avoid ordering. Experiments on another symmetric SISO tetrablock polymer described elsewhere53 show that the LLP phase is generated when the sample is quenched sufficiently far below TODT (Figure S2a and see below). Upon increasing τ further, the resulting SIS′O-0.61 and SIS′O-0.70 tetrablocks exhibit very similar behavior. From 120 to 160 °C, SAXS patterns for SIS′O-0.61 display two broad peaks indicating limited long-range structural order attributed to the LLP state (Figure 5a). At higher temperatures, SIS′O-0.61 has a SAXS pattern with three closely spaced strong peaks, along with a lower intensity peak at lower q, all centered around the same position where the q* peak dominates at lower temperature. These peak positions and relative intensity distributions are shown in Figure S2b to derive from a dodecagonal quasicrystal (DDQC).25,53 The same pattern is observed for SIS′O-0.70 from 140 – 150 °C. Upon further heating to 170 °C for SIS′O-0.61 and 160 °C for SIS′O-0.70, the scattering pattern transforms into one characteristic of the σ phase. Both samples disorder around 180 °C (Figures 5a and S3a).


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Figure 5. (a) SAXS patterns from SIS′O-0.61 starting from a freeze-dried state. The sample was annealed overnight at 120 °C and quenched in LN2; the polymer exhibited broad peaks attributed to the LLP phase when heated back to 120 °C. Upon heating, patterns consistent with the DDQC and σ phases are observed before disordering. (b) TEM image obtained from the sample annealed at 120 °C displays limited long-range order within the specimen with regions of short-range periodic order, consistent with LLP spheres. (c) Annealing at 170 °C for one day reveals a morphology consistent with the σ phase. Note that the phases seen here are also observed in SIS′O-0.73 when its temperature ramp is started from 260 °C.

TEM analysis of SIS′O-0.61 at 120 °C led to micrographs showing limited long-range order in the specimen but with some degree of short range order, consistent with the LLP assignment (Figure 5b). Images acquired from SIS′O-0.70 at 170 °C contain tiling elements consistent with the σ phase (Figure S3b). Curiously, annealing SIS′O-0.70 at 140 °C for an extended period (24 h) reveals images inconsistent with any of the observed SAXS patterns (a representative micrograph is shown in Figure 6c). One candidate morphology consistent with these images is the A15 phase (space group 3), which has been experimentally reported in the proximity of the σ phase in several soft and hard materials including supramolecular dendrimers and transition metal alloys.54,55 Although the A15 phase has been anticipated in branched and conformationally asymmetric linear diblocks using SCFT simulations,23,56 these predictions have only been experimentally verified in dendritically branched diblocks57 to the best of our knowledge.


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Figure 6. (a) Unit cell and (b) structure model of the A15 phase tiling viewed along the [001] direction and corresponding simulated diffraction pattern (inset). (c) TEM micrograph obtained from SIS′O-0.70 tetrablock terpolymer after annealing for one day at 140 °C and corresponding FFT (inset). (d) Simulated density plots for O, I, S′ (interior), and S (terminal) blocks in the xy-plane at z=1/2 in the A15 phase of the SIS′O tetrablock terpolymer. The calculations are done at T = 180 °C, fO = 0.13 with parent triblock SIS′ molecular weight, M = 20.8 kDa.

Figure 6 illustrates the unit cell of the A15 phase along with the corresponding tiling of the [001] projection. The tiling and its simulated diffraction pattern are strikingly similar to the TEM micrograph observed in the annealed SIS′O-0.70 samples and its Fourier transform. Appearance of the A15 phase, combined with the widening of the window for sphere forming phases from SCFT simulations, prompted a more detailed theoretical and experimental investigation of modestly asymmetric ( 0.7) SIS′O tetrablock terpolymers. In order to elucidate the positions of each block in the SIS′O-0.73 tetrablock, density plots were generated for the A15 unit cell using SCFT results. Figure 6d depicts the density profiles of the O, I, interior S′, and terminal S blocks in the xy plane sliced at z = ½ of the A15 unit cell. The density profiles for the O and I blocks are intuitive and confirm that O forms the core while I fills the matrix. Unsurprisingly, the density plot for the interior S′ shows that this block mainly forms a shell to shield the O blocks from the I blocks, which are associated with the largest and most energetically unfavorable 13 ACS Paragon Plus Environment

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segment-segment interactions. However, some amount of terminal S is also present in the shell to further the shielding, while the rest fills the matrix along with I. Perhaps the most interesting observation in Figure 6d is that the matrix-forming I and terminal S blocks exhibit a moderate amount of segregation and a non-uniform spatial distribution that reflects the lattice symmetry.

As shown in Table 1, SIS′O-0.68 and SIS′O-0.73 are similar in O content and molecular symmetry to SIS′O-0.70. However, the relatively higher molecular weight of these two samples leads to higher (> 100 °C) order-disorder transition temperatures for these two samples than for SIS′O-0.70, which permits deeper quenches from TODT before chain dynamics are impeded due to strong segregation (and eventually vitrification of polystyrene chains). Along with this advantage, polymer degradation is a concern at such high temperatures, especially due to the presence of poly(isoprene). SEC traces obtained following the most severe thermal treatments (T > 250 °C for 2 hours) demonstrate some broadening of the distribution of molecular weights (Figure S4). Nevertheless, heating and cooling through TODT did not affect the transition temperature as determined by SAXS and dynamic mechanical spectroscopy (DMS), indicative of limited impact of chain degradation.


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Figure 7. Synchrotron SAXS patterns at selected temperatures during (a) heating ramp (~1 °C/min) of SIS′O-0.73 starting at 120 °C. The tetrablock was freeze-dried from benzene and received no thermal treatment prior to the experiment. An unknown phase with possible rhombohedral symmetry (based on TEM experiments) is seen at 120 °C. Heating drives a transition to the HCP, A15, σ, and disordered phases. (b) SAXS patterns during a heating ramp starting at 260 °C for the same sample show different behavior. Patterns are consistent with the DDQC phase after a short anneal at 260 °C which transitions to σ at higher temperatures before disordering.

Rheological measurements reveal that the SIS′ precursor remains disordered over the entire temperature range (85 °C – 285 °C) utilized in the scattering experiments (Figure S5). Scattering data on SIS′O-0.68 and SIS′O-0.73 show very similar behavior upon heating (presented in Figures S6 and 7, respectively). Heating a freeze-dried specimen of SIS′O-0.73 to 120 °C leads to three well-defined but relatively broad peaks at (q/q*)2 = 1, 2, and 5. TEM analysis of this material annealed at 120 °C for 10 minutes reveals grains composed of spheres (particles) with periodic order. A FFT of these images displays “stretched” hexagons which is consistent with rhombohedral order and compatible with the observed SAXS peak ratios (Figure S7). However, the assignment of a space group and detailed structural information cannot be addressed here due to an insufficient number of Bragg peaks. Additional experiments indicate that this structure is stable and largely recovered when cooling from any other temperature. Heating to 160 °C transforms the morphology to one consistent with an HCP phase (space group P63/mmc) as shown in Figure 7a; a detailed listing of peak assignment and associated lattice parameters are 15 ACS Paragon Plus Environment

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presented in Table S1. Further heating to 240 °C leads to a scattering pattern that cannot be indexed based on any previously reported block copolymer morphology but is similar to those reported in thermotropic and lyotropic micelles for the A15 phase (space group 3).31,58 A detailed analysis of the diffraction data reveals quantitative agreement with an A15 assignment, as shown by the allowed reflections labeled in Figure 7a and listed in Table S1. TEM micrographs obtained from SIS′O-0.73 annealed at 220 °C for 1 hour (Figure S8) compare favorably with a square tiling of the [001] projection of the A15 structure, and are consistent with the TEM image from SIS′O-0.70 (Figure 6c). These real space TEM images combined with the reciprocal space SAXS patterns firmly establish the 3 space group and confirm the existence of the A15 phase within the SIS′O system at temperatures moderately below TODT. Heating SIS′O-0.73 further to 280 °C drives a transition to the σ phase, a structure now wellestablished in both tetrablock and diblock copolymers (detailed structural information is presented in Table S1).22,25 The sample disorders around 284 °C. SAXS experiments show that the same transitions are observed in SIS′O-0.68: TRhomb < THCP < TA15 < Tσ < TDIS (Figure S6); detailed structural information for this sample is presented in Table S2. Upon cooling from the disordered phase, the σ, HCP and rhombohedral (tentatively assigned) phases are recovered but the A15 phase is not seen (Figure S6). SAXS traces also reveal that BCC order is briefly encountered close to TODT as a transient phase before growth of σ from the disordered phase (Figure S6).

Strikingly different phase behavior was obtained from a freeze dried SIS′O-0.73 sample rapidly heated (~130 °C/min) to 260°C before subsequent heating through TODT (Figure 7b). Upon reaching 260 °C, the sample produced broad peaks similar to those seen in SIS′O-0.61 corresponding to the LLP phase. Note that the same sample displays reflections consistent with 16 ACS Paragon Plus Environment

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the A15 phase when heated slowly to 260 °C from a starting temperature of 120 °C (Figure 7a). After annealing for five minutes, a characteristic set of 4 reflections develop, with a low intensity peak at lower q adjacent to a triplet of higher intensity peaks. The same pattern is observed in SIS′O-0.61 at 160 °C, attributed to growth of the DDQC phase based on analogous scattering from DDQC forming dendrimers (see Figure S2b) and poly(isoprene)-b-poly(lactide) (IL) diblock copolymers as described elsewhere.59,60 Further heating to 280 °C and 180 °C for SIS′O0.73 and SIS′O-0.61, respectively, drives a transition to the σ phase before a single, broad peak is observed for both samples upon raising the temperature beyond TODT. Additionally, annealing SIS′O-0.73 overnight at 140 °C reveals the presence of yet another phase not observed when the sample is heated to 140 °C from a freeze-dried state without annealing. SAXS patterns for the annealed sample indicate reflections consistent with a mixture of HCP and FCC morphologies as shown in Figure S9. The fascinating richness in the phase behavior of these SIS′O samples as a function of τ and thermal processing is summarized in Figure 8. While we have not exhausted all possible processing scenarios for this set of materials (for example, we overlooked cooling SIS′O-0.21, SIS′O-0.32, and SIS′O-0.39 from T > TODT to confirm growth of the HEXS phase), the overall compliment of experimental and theoretical results reported here, and previously,22,25,51,52 provide a concrete basis for rationalizing the equilibrium and nonequilibrium phase behavior associated with asymmetric ABA′C type tetrablock terpolymers when χAB ≅ χAC > χSO ≅ χIS, drives formation of core-shell spheres at the compositions examined in this study.52 The molecular architecture mandates the presence of an S′ shell around the O core at all temperatures, which screens the most enthalpically costly O-I contacts at all temperatures below the mean-field limit, TMF >> TODT. Cooling towards and below TODT from a high temperature increases block segregation. Near TODT the continuous matrix of S and I blocks (and to a lesser extent S′ blocks) are relatively uniformly distributed in space around the O core. In this limit we believe the tetrablock terpolymer behaves like a pseudo diblock, [SIS′]-O, as depicted in Figures 9a and 9b. Moreover, in this regime the molecules can undergo chain exchange, allowing the system to equilibrate over experimentally accessible times, analogous to the behavior of IL diblocks that form the Frank-Kasper σ phase within 20 to 30 °C of TODT.8,60 With the exception of SIS′O-0.21 and SIS′O-0.32 (where the HEXS phase is adjacent to the disordered state) the σ phase is obtained near TODT upon heating from the freeze-dried state or cooling from the disordered state. This reversibility is consistent with our equilibrium argument. Absence of the σ phase in the lowτ tetrablocks underscores the importance of the molecular symmetry in guiding the formation of specific equilibrium morphologies.


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Figure 9. Schematic illustration of the hypothesized effect of temperature on the nature of SIS′O particles. (a) and (b) Close to TODT, the spheres possess a mobile core facilitating chain exchange and driving the formation of equilibrium disorder and σ phases. (c) However, below Terg, stronger segregation between S and I arrests chain exchange immobilizing the core and leading to the formation of non-equilibrium morphologies.

Cooling the pseudo-diblock strengthens segregation of O from [S′IS] and segregation of S from I in the coronas, thus reducing the rate of chain exchange (Figure 9c). Our recent investigation of IL diblocks has revealed that below a specific temperature, denoted Terg, the supercooled disordered material becomes non-ergodic due to the catastrophic effects of restricted chain diffusion.60 (Here we note that the consequences of reducing the temperature below Terg should not be confused with the effects induced when approaching Tg of the particle core, which also arrests chain exchange.8 In the present case, the O cores have a glass transition temperature (Tg,O) far below the temperatures accessed in the experiments). We believe that the thermal processing history dependence exhibited by the SIS′O materials at low temperatures reflects metastable


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states associated with restricted tetrablock diffusion when T < Terg. Arresting chain exchange shifts the ordering mechanism to one dominated by S-I-S′ matrix segregation coincident with the appearance of non-equilibrium morphologies. Structure formation within this non-equilibrium regime is mediated by the matrix as mass exchange by overall chain diffusion and particle-level dynamics (e.g., translation, fusion, evaporation, etc.) are “frozen” out. Segregation of the I and S blocks within the matrix is supported by SCFT simulations as revealed by Figure 6d for the A15 phase in SIS′O-0.73 at 180 °C, approximately 100 °C below TODT. The confinement of the O and interior S′ blocks to the core and shell, respectively, is evident from the density distribution. Interestingly, the I and terminal S blocks still display significant mixing around 180 °C. However, cooling the material increases segregation within the S-I-S′ matrix which, in turn, may guide ordering of the spheres, leading to the formation of distinct domains for each block and a different state of order for the particles. Importantly, at all measurement temperatures (T ≥ 120 °C) the blocks that make up the S′IS matrix are always far above the glass transition temperature (Tg, matrix < 70 °C) due to the effects of mixing poly(isoprene) (Tg,I = -70 °C) with poly(styrene) (Tg,S = 100 °C). Thus, as the temperature is lowered, the HCP and (tentatively assigned) rhombohedral phases occur primarily as a consequence of increased spatial segregation between the I and S blocks. Both phases can be obtained by rapidly cooling from the pseudo-diblock regime or heating from a freeze-dried state. This matrix based metastable ordering obviates the sphericity arguments associated with the symmetry breaking that is speculated to produce the equilibrium Frank-Kasper σ phase.8 Thus, we hypothesize that ordering in the tetrablock terpolymer system can be categorized under two temperature dependent regimes: the chain exchange mediated pseudo-diblock regime and the non-equilibrium regime governed by matrix segregation. The latter is a direct consequence of the multiblock molecular architecture, which


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introduces additional internal degrees of freedom (not available to diblocks) with which to tailor the phase behavior of these nominally single component materials.

As demonstrated, the equilibrium morphologies associated with the pseudo-diblock regime can be obtained by heating from a freeze-dried state or cooling from the disordered state. Similarly, with the exception of the FCC state (which competes with HCP upon heating freeze dried SIS′O0.73 to 140 °C; see Figure S9), phases in the non-equilibrium regime can also be obtained by heating from a freeze-dried state or cooling from the disordered phase (see Figure 8). However, within these two limiting regimes lies a transition zone comprised of metastable phases, including LLP, DDQC, and perhaps A15, whose formation is strongly path dependent. As Figure 7b illustrates, within SIS′O-0.73, the LLP state is only found when the sample is rapidly heated to 260 °C. The heating ramp from this starting temperature mirrors the results seen for SIS′O0.61 (Figure 5a). In both samples, the LLP state is obtained by rapidly heating a sample from the freeze-dried state (or rapidly cooling SISO specimens from the disordered state; see Figure S2). Subsequent heating renders the DDQC followed by the σ phase before disordering. The appearance of these phases parallels recent findings in poly(isoprene)-b-poly(lactide) (IL) diblocks.60 The kinetically trapped LLP state is obtained in this diblock by quenching the disordered liquid rapidly enough and sufficiently far below TODT to avoid ordering (as opposed to heating from the freeze-dried state) which coincides with the results shown in Figure S2a for a SISO tetrablock. The LLP state likely contains some form of short-range polytetrahedral order,60 which eventually spawns the DDQC. Given enough time, the equilibrium σ phase is able to nucleate and grow through chain exchange and, perhaps, other particle-level relaxation processes.60


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When rapidly heated to 120 °C and 260 °C, freeze dried specimens of SIS′O-0.61 and SIS′O0.73, respectively, evolve virtually identical phase behavior with subsequent heating. SIS′O-0.73 (and SIS′O-0.68) was designed to provide access to deeper quench depths. Frankly, we were surprised to discover that the LLP and DDQC phase could be accessed by rapid heating to a comparable temperature below TODT. Even more surprising is the occurrence of the A15 phase at around 240 °C when SIS′O-0.73 is heated from 120 °C (Figure 7a). These experiments reveal a pronounced path dependence to the morphology, which we associate with the transition from ergodic to non-ergodic behavior. The A15 phase is observed only when heating from the HCP phase and does not appear when the sample is cooled from the σ or disordered phases. Upon heating, as chain exchange becomes a viable diffusion mode with decreasing segregation strength, the formation of A15 may facilitate a transition between the non-equilibrium HCP and equilibrium σ phases.61 The restriction of filling space at constant density necessitates distortions of the spherical tetrablock particles into distinct polyhedra of various shapes and sizes, i.e., Wigner-Seitz cells, as dictated by the lattice symmetry. The A15 lattice requires two different polyhedra and bridges the HCP phase, which requires only one polyhedron, to the σ phase, which requires five distinct polyhedral shapes and sizes for the particles.62 During the cooling experiment, matrix segregation guides the assembly of the particles, leading to formation of the HCP phase from the σ phase without an A15 intermediate. Additionally, SAXS patterns recorded by heating SIS′O-0.70 to 140 °C from a freeze-dried state indicate formation of the DDQC morphology within 5 minutes, while annealing the sample for one day at the same temperature reveals clear TEM images of the A15 phase, suggesting this may be an equilibrium state at segregation strength slightly greater than that required to produce the σ phase (SCFT calculations on conformationally asymmetric diblocks anticipate this scenario).23 These experiments highlight


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the extraordinary sensitivity to small variations in molecular architecture and state properties along with the roles of metastability and path dependence in the formation of terpolymer morphologies. Despite the rich phase behavior already observed, multiblock polymer theory,63 along with the demonstrated process path dependence, leads us to anticipate the discovery of additional equilibrium and metastable phases with variations in tetrablock composition, molecular weight and thermal treatments.

In some respects, the transition regime identified in Figure 8 may be the most intriguing part of the phase map shown. Here the effects of diffusion limitations are most pronounced, mediating the formation of specific phase symmetries, most remarkably the DDQC. At this point we cannot ascertain which phases exist in equilibrium at temperatures below those where the Frank-Kasper σ phase is clearly most stable. SCFT suggests that the sequence A15→σ→BCC→disorder should be observed with heating in conformationally asymmetric copolymers.23 Our theoretical calculations indicate extreme sensitivity to the precise assignment of the χ parameters, which have different temperature and composition dependencies. This work provides unambiguous evidence as to the importance of combining quantitative theory (and simulation) with exacting polymer synthesis and precise structural characterization in pursuing the extraordinary opportunities presented by multiblock polymers.

Conclusions

Self-consistent field theory (SCFT) calculations combined with precise synthesis and quantitative structural characterization have revealed an extraordinary array of ordered states in sphere forming linear poly(styrene)-b-poly(isoprene)-b-poly(styrene)′-b-poly(ethylene oxide) (SIS′O) tetrablock terpolymers. A molecular symmetry parameter, = /( + ) in which 25 ACS Paragon Plus Environment

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NS and NS′ are the degrees of polymerization of the terminal and interior poly(styrene) blocks, respectively, is shown to influence the formation of nine discrete states of order in this class of multiblock polymers. Equilibrium and metastable morphologies are associated with temperature regimes near the order-disorder transition (TODT), and T

Cornucopia of Nanoscale Ordered Phases in ... - ACS Publications

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